I have pictures and I have questions

I hope you can see those but I just hit back from my first harder ride in a month. 23 miles in 1 hour 12 minutes, Average speed 19.3 mph. But I don't know my cadence or understand my rpm. While riding my rpm was ranging from 23o- 3oo rotations per minute .I know I was in a good gear because I want spinning with out resistance? I rarely used the larger gear on the crank mainly stayed in the second, I thought this might be a cause so I went on a second ride. I put it in the largest ring on the crank and shifted the gears up. But with every shift the rpms increased? Why?

Shift up - go larger on front chainring, go small on rear cogs. Go faster with less rpm.

If you shift into larger gears on the RD, your RPM will increase and pedaling will be easier and faster. An RPM of 110 is pretty fast, are you sure your crank RPM were two hundred thirty?

FB4K - This December, 2014, 5288 kids received bikes for Christmas. For many, it was their first bike, ever. Every bike, new and used, was donated, built, cleaned and repaired. That amounts to well over 10,000 volunteer hours this fall, just in the Twin Cities. Check us out on FaceBook: FB4K.
Disclaimer: 99% of what I know about cycling I learned on BF. That would make, ummm, 1% experience. And a lot of posts.

According to a gear calculator I use (Bicycle Bike Gear Ratio Speed and Cadence Calculator), to manage 230+ cadence and only average ~19mph, the gear you'd need to be in is 30x30 the entire time (so you'd need a compact triple front and a 12-30 rear cassette). Since you say you put it in the "largest" ring that would likely be a 50, so 19mph in 50x30 is 145rpm. (Also your FD would likely rub like mad the entire time since you are max cross-chained in this gear).

Sounds like whatever you're using for cadence information is doubling your rpm data.